Early detection of Alzheimer's disease is essential for more effective patient care. This study explores the application of Machine Learning (ML) algorithms in detecting Alzheimer's disease by analyzing influential factors, such as demographic profile, medical history, and clinical examination results. Five ML methods, namely Deep Learning, Random Forest, Decision Tree, Naïve Bayes, and Logistic Regression, are used to classify Alzheimer's disease cases. In addition, the study used RFE and BPSO methods for feature selection with the aim of improving model performance. The evaluation was conducted using cross-fold validation and split-validation techniques, with performance measured in terms of accuracy, precision, recall, and F1-score. The results showed that the Random Forest algorithm combined with BPSO achieved the best performance, with 99% accuracy and high precision and recall values, surpassing other methods. These findings demonstrate that integrating feature selection significantly improves classification quality and confirms the practical potential of ML models as reliable tools for the early detection of Alzheimer's disease, thereby assisting clinicians in diagnostic decision-making and enhancing patient care.